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Table 7 Results on stable L1-structures

From: A replica exchange Monte Carlo algorithm for protein folding in the HP model

ID

E*

PERM t e x p MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabdwgaLjabdIha4jabdchaWbqabaaaleqaaaaa@373A@

REMC pm

REMC m

L1-1-3

-16

-16 (120 sec)

-16 (6 sec)

-16 (6 sec)

L1-2-2

-16

-16 (57 sec)

-16 (3 sec)

-16 (2 sec)

L1-3-1

-16

-16 (28 sec)

-16 (3 sec)

-16 (3 sec)

L1-1-5

-24

-24 (100 hrs†)

-24 (17 min)

-24 (14 min)

L1-2-4

-24

-24 (49 hrs†)

-24 (9 min)

-24 (7 min)

L1-3-3

-24

-23

-24 (7 min)

-24 (5 min)

L1-4-2

-24

-24 (49 hrs†)

-24 (5 min)

-24 (4 min)

L1-3-7

-40

-38

-38 (20 hrs)

-38 (20 hrs)

L1-5-5

-40

-38

-38 (16 hrs)

-38 (14 hrs)

L1-8-2

-40

-38

-38 (16 hrs)

-38 (14 hrs)

  1. The L1-structures proposed in [52] are the most difficult stable structures for REMC to fold. Both PERM and REMC are unable to find the optimal conformations for L1-3-7, L1-5-5, and L1-8-2 after 100, one hour runs. PERM also did not find the optimal conformation for L1-3-3. When only one folding direction of PERM finds the optimal conformation, we report the mean run-time of that direction, denoting this in the table with a †. When best energies found by PERM t 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabigdaXaqabaaaleqaaaaa@33F5@ and PERM t 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabikdaYaqabaaaleqaaaaa@33F7@ differed (and neither find the optimal solution), the best energy by either is reported and the run-time is omitted. For every instance, 100 independent runs were conducted of 1 CPU hour each. In cases where not every run reached the same energy value after 1 hour, the expected run-time to reach the energy value shown in the table was calculated using the equation detailed by Parkes and Walser [54].